Evaluating the Egyptian HARN Network by GNSS Precise Point Positioning “PPP”

International Journal of Scientific & Engineering Research, Volume 6, Issue 6, June-2015 858 ISSN 2229-5518

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Evaluating the Egyptian HARN Network by GNSS Precise Point Positioning “PPP” Mostafa Rabah*, Mahmood Elmewafey**, Magda H. Farahan***, Ahmed Awad** and Ali. Jaafar**

*: National Research Institute of Astronomy & Geophysics, **: Faculty of Engineering, Mansura University

***: Faculty of Engineering, Kafr Elsheikh University

Abstract: One of the fundamental goals of geodesy is to precisely define positions of points on the surface of the Earth, so it is necessary to estab-

lish a well-defined geodetic datum for geodetic measurements and positioning computations. Recently, a set of the coordinates established by using GPS and referred to an international terrestrial reference frame could be used as a three-dimensional geocentric reference system for a country. Based on this modern concept, in 1992, the Egypt Survey Authority (ESA) established two networks. The first net is called High Accu-racy Reference Network (HARN) and consisted of 30 stations, 200 km spacing. The second network was established to cover the cultivated areas (Nile Valley and Delta) so it is called the National Agricultural Cadastral Network (NACN) with spacing 30 to 40 km. To transfer the Inter-national Terrestrial Reference Frame to the HARN, the HARN was connected with four IGS stations. The processing results were 1:10,000,000 (Order A) for HARN and 1:1,000,000 (Order B) for NACN relative network accuracy standard between stations defined in ITRF1994 Epoch 1996.

To evaluate the HARN & NACN, a co-joint team from NRIAG and Mansura University observed the available HARN & NACN stations in the Nile Delta. The Processing of the tested part was done by CSRS-PPP Service based on utilizing Precise Point Positioning “PPP” and Trimble Business Center “TBC”. The study shows the feasibility of Precise Point Positioning in updating the absolute positioning of the HARN network and its role in updating the reference frame (ITRF). The study also confirmed the necessity of the absent role of datum maintenance of Egypt networks.

Keywords: ITRF, PPP, Geodetic Datum, HARN, DGPS, IGS, Transformation Parameters.

—————————— —————————— 1 INTRODUCTION

n space geodetic positioning, where the observation tech-niques provide absolute positions with respect to a con-sistent terrestrial reference frame, the corresponding precise

definition and realization of terrestrial and inertial reference systems is of fundamental importance. Thanks to significant improvements in receiver technology, to extension and densi-fication of the global tracking network along with more accu-rate determination of positions and velocities of the tracking stations and to dramatically improved satellite orbits, GPS is today approaching 0.1 ppm precision for longer baselines and it can be considered to be the main global geodetic positioning system providing nearly instantaneous three-dimensional po-sition at the cm accuracy level. One of the fundamental goals of geodesy is to precisely define positions of points on the sur-face of the Earth, so it is necessary to establish a well-defined geodetic datum for geodetic measurements and positioning computations. Recently, a set of the coordinates established by using GPS and referred to an international terrestrial reference frame could be used as a three-dimensional geocentric refer-ence system for a country [1]. In the classical sense, a geodetic datum is a reference surface, generally an ellipsoid of revolution of adopted size and shape, with origin, orientation, and scale defined by a geocentric ter-restrial frame. Once an ellipsoid is selected, coordinates of a point in space can be given in Cartesian or geodetic (curviline-ar) coordinates (geodetic longitude, latitude, and ellipsoid height).

Two types of geodetic datum can be defined namely a static and kinematic geodetic datum. A static datum is thought of as a traditional geodetic datum where all sites are assumed to have coordinates which are fixed or unchanging with time.

This is an incorrect assumption since the surface of the earth is constantly changing because of tectonic motion. Static datum does not incorporate the effects of plate tectonics and defor-mation events. Coordinates of static datum are fixed at a refer-ence epoch and slowly go out of the date, need to change peri-odically which is disruptive.

Datum's can either become fully kinematic (dynamic), or semi-kinematic. A deformation model can be adopted to ena-ble ITRF positions to be transformed into a static or semi-kinematic system at the moment of position acquisition so that users do not see coordinate changes due to global plate mo-tions. GNSS devices which use ITRF or closely aligned sys-tems position users in agreement with the underlying kine-matic frame, however, in practice there are a number of very significant drawbacks to a kinematic datum. Surveys under-taken at different epochs cannot be combined or integrated unless a deformation model is applied rigorously, or is em-bedded within the data, and the data are correctly time-tagged. On the other hand, Semi–Kinematic datum incorpo-rates a deformation model to manage changes (plate tectonics and deformation events). Coordinates fixed at a reference epoch, so the change to coordinates is minimized. Many coun-tries and regions which straddle major plate boundaries have adopted a semi-kinematic (or semi-dynamic) geodetic datum in order to prevent degradation of the datum as a function of time due to ongoing crustal deformation that is occurring within the country.

High precision GNSS positioning and navigation is very rapidly highlighting the disparity between global kinematic reference frames such as ITRF and WGS84, and traditional static geodetic datum. The disparity is brought about by the

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increasingly widespread use of PPP and the sensitivity of these techniques to deformation of the Earth due to plate tec-tonics. In order for precision GNSS techniques to continue to deliver temporally stable coordinates within a localized refer-ence frame.

2. Transformation Parameters Terrestrial Reference Systems “TRS”

Transformations from kinematic ITRF to a static datum are conventionally done by either using the site velocity (meas-ured directly or computed from a plate motion model) to compute the displacement between the reference and current epochs or by a conformal transformation augmented with time dependent parameters to account for rigid plate motion. Rigid Plate movement is conventionally defined by a rotation rate about an Euler Pole Φ,Λ and ω, where Φ, Λ are the lati-tude and longitude of the pole, and ω is the rate of rotation of the plate around the pole in degrees per million years. Equiva-lent rotation rates about the Cartesian axes (ΩX,ΩY and ΩZ) can be computed from the Euler pole definition using equations (1-3) (Φ,Λ, and ω) are first converted from decimal degrees to radians)[2]:

Ω𝑋 = cos(Φ) cos(𝛬)𝜔 (1) Ω𝑌 = cos(Φ) sin (𝛬)𝜔 (2) Ω𝑍 = sin(Φ)𝜔 (3)

A site velocity in Cartesian format (X., Y. , Z.) can be com-puted for any given location (X, Y, Z in meters) on a rigid plate defined by (Ω𝑋, Ω𝑌, Ω𝑍 ) in radians per million years) using:

�𝑋 .

𝑌.

𝑍 .� = �

Ω𝑌𝑍 −Ω𝑍𝑌Ω𝑍𝑋 −Ω𝑋𝑍Ω𝑋𝑌 −Ω𝑌𝑋

�. 1E-6 (4)

By introducing a reference epoch t0 and an epoch of measure-ment t (epochs in decimal years), the ITRF coordinates of any point on a rigid plate at a reference epoch (X0,Y0,Z0 in meters) can be computed from the coordinates at epoch t (Xt, Yt , Zt in meters) using:

�𝑋0𝑌0𝑍0� = ��

𝑋𝑡𝑌𝑡𝑍𝑡�+ �

Ω𝑌𝑍𝑡 −Ω𝑍𝑌𝑡Ω𝑍𝑋𝑡 − Ω𝑋𝑍𝑡Ω𝑋𝑌𝑡 − Ω𝑌𝑋𝑡

� . (𝑡0 − 𝑡)1E − 6� (5)

For any location on a rigid plate, instantaneous ITRF coordinates can be transformed to a fixed reference epoch using equation (5-18) (Stanaway and Roberts, 2009).

�𝑋0𝑌0𝑍0� = �

𝑇𝑋𝑇𝑌𝑇𝑍�+ 𝑆. ��

𝑋𝑡𝑌𝑡𝑍𝑡�+ �

Ω𝑌𝑍𝑡 − Ω𝑍𝑌𝑡Ω𝑍𝑋𝑡 −Ω𝑋𝑍𝑡Ω𝑋𝑌𝑡 −Ω𝑌𝑋𝑡

� . (𝑡0 − 𝑡)/1000000�

(6) Where:

(𝑋0,𝑌0,𝑍0): are the ITRF Cartesian coordinates at the reference epoch 𝑡0 (in decimal years),

(𝑋𝑡 ,𝑌𝑡 ,𝑍𝑡): are instantaneous ITRF Cartesian coor-dinates at epoch 𝑡 (epoch in decimal years),

(𝑇𝑋 ,𝑇𝑌 ,𝑇𝑍): is the translation of the reference frame origin (from ITRF to local system),

(Ω𝑋 ,Ω𝑌 ,Ω𝑍): are the Cartesian rigid plate/block rota-tion parameters, is the reference frame

𝑆: is scale factor (from ITRF to local). The African continent is broadly divided into two major

tectonic plates. Most of Africa, west of the East African Rift lies on the Nubian Plate. The Somalian Plate lies east of the Afri-can Rift. A very small section of North Africa along the Ma-ghreb coast in Algeria and Morocco lies on the Eurasian Plate and the Dankalia region of Eritrea lies on the Arabian Plate.

Analysis of the ITRF2005 solution [3]; [4] indicates that ITRF site velocities for any location within Africa are between 24 and 31 mm/yr due to rigid motion of the African plates over the underlying mantle. These site velocities degrade the accuracy of absolute positions like PPP if the measurement epoch is misinterpreted as a reference epoch for the underly-ing datum realization in use at the time Equations (1, 2 and 3) were used to compute(ΩX, ΩY, ΩZ) for the Nubian Plate using the Euler parameters determined by ITRF2008 PMM “Plate Motion Model” [5], the results were depicted in table (1).

Table (1): The Cartesian angular Velocity of Nubian Plate Deformation

Model Absolute Pole Cartesian angular Velocity

for Nubian Plate 𝛀𝐗 (Rad/Ma) 𝛀𝐘 (Rad/Ma) 𝛀𝐙 (Rad/Ma)

ITRF2008-PMM 0.000461 -0.00290 0.003506

3. PPP Solution PPP has received increased attention in the past several

years within the GPS community due to its great operational flexibility and accuracy promise. The major advantages of PPP lie in two aspects: system simplicity at the user’s end and global consistency in terms of positioning accuracy. PPP-based approach significantly reduces the equipment and personnel costs, pre-planning, and logistics compared to conventional GPS network-based approaches. Applying PPP, a single sur-vey team can establish a CORS network across a PPP has re-ceived increased attention in the past several years within the GPS community due to its great operational flexibility and accuracy promise [6].

The major advantages of PPP lie in two aspects: system simplicity at the user’s end and global consistency in terms of positioning accuracy. PPP-based approach significantly reduc-es the equipment and personnel costs, pre-planning, and logis-tics compared to conventional GPS network-based approach-es. Applying PPP, a single survey team can establish a control network across a large area, rather than the complicated logis-tics and communications needed to organize multiple survey teams to occupy stations simultaneously. It also reduces the needs to analyze the data using scientific software packages, which are not generally too accessible to inexperienced users.

Measurements from the IGS global tracking network are processed by the IGS Analysis Centers to provide the highest quality satellite orbit and clock parameters. These parameters are freely available from the Internet and are the basis for PPP development. These IGS products can be applied to signifi-cantly reduce the errors in GPS satellite orbits and clocks, which are two of the most significant error sources in GPS positioning. Combining precise satellite positions and clocks with a dual frequency GPS receiver to remove the first order effect of the ionosphere, PPP is able to provide position solu-tions at centimeter level. Coordinates estimated with PPP will

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be in the same global reference frame as the satellite orbits. When using orbits from IGS, estimated receiver coordinates are referred to the IGS realization of ITRF.

Last decades several PPP post-processing software have been developed based on the above observation models. Also online web services from different organizations such as the Precise Point Positioning Software Center (http://gge.unb.ca/Resources/PPP/index.htm) which has been created under the auspices of the Canadian Geomatics for In-formed Decisions Network of Centers of Excellence provides users easy access to online PPP services as CSRS-PPP by Nat-ural Resources Canada (NRCan),GPS Analysis and Position-ing Software (GAPS) by University of New Brunswick (UNB), Automatic Precise Positioning Service(APPS) by Jet Propul-sion Laboratory (JPL), and magic GNSS by GMV (privately owned technological business group).

EVALUATING THE PPP SOLUTION The solution of CSRS-PPP SW is now used extensively to

provide realizations of ITRF globally with a precision of a few centimeters. Four groups of data from IGS stations, namely MALI (Malindi, Kenya) on the Somalian plate, RABT (Mo-racco) on the Nubian plate, RAMON (occupied Palestine) on the Arabian plate and NICO (Nicosia, Cyprus) on the Eurasian plate, distributed over the different sub-plates of Africa and their positioning was computed and published by the IGS da-ta centers at ITRF 2008 Epoch2005 and given in table (2). The data of the four groups of IGS stations was downloaded from ftp://garner.ucsd.edu/pub/rinex/2015/100/ for Day 100, 2015 and processed using the Precise Point Positioning module of CSRS-PPP. To transfer the IGS published coordinates from Epoch2005, as: t0= 2005, to the epoch of the PPP solutions, ITRF 2008 Epoch2015.274 as t, Epoch2015.274, the following formula [7], is used:

P ( t0 ) = P( t ) + P˙( t0- t ) (7) Where:

P(tR0R) = is the positioning at a reference epoch ITRF 2008 Epoch 2005

P(t) = is the positioning value at time t, defined by PPP at epoch 2015.274

P˙ = Velocity

The transferred coordinates of the four IGS stations defined in ITRF2008 Epoch 2015.274 are tabulated in table (3) as comput-ed by IGS 5TUhttp://itrf.ign.fr/.U5T

To see how the PPP can be used in updating the ITRF of the IGS points, the solution of PPP with the transferred pub-lished IGS ITRF2008 at Epoch 2015.274 are given in table (4). The differences between two solutions are computed and out-lined in table (4). As it is shown in the table, the absolute value of the maximum differences does not exceed 17mm for the Y component of Nico Station, while does not exceed few mm for the other stations.

By comparing the differences of the two solutions for the four IGS stations, one can easily see that, how the PPP is pre-cise in expressing the epochwise solution of the ITRF frame.

Additionally to see for what extent PPP can be an alternative for the differential techniques, seven test points were pro-cessed by Trimble Business Center “TBC” Software, the prod-uct of Trimble, with considering the PPP solution of PHLW as a reference station for the processing. The results of the pro-cessing were demonstrated in table (5). As it is shown in table (5), one can easily see the quality of PPP solution compared with the DGPS solution. In spite of the processed baselines are exceed several tens of kilometers to 120 km, PPP shows good harmony with the DGPS in mm level except the station 0Z20 which has differences of 2.3 to 3.2 cm that may be it has the longest baseline as well as it gives the worst accuracy of PPP that is may become from the surround-ing environments around the station.

4 THE EVALUATION STUDY In 1992, an ESA steering committee developed a plan for the creation of new datum for Egypt, with the following approach [8]:

• First, observe approximately 30 stations at approxi-mately 200 km interval, covering all of Egypt, creating a High Accuracy Reference Network (HARN). Both high absolute and relative accuracies are required for these stations.

• Second, establishing the Notational Agricultural Ca-dastral Network (NACN) relative to these 30 stations, covering the green area of Egypt (Nile Valley and the Delta) at 30-40 km intervals. This station spacing was selected to allow for further densification with single frequency receivers, see figure (1).

• Third, densify this network at a station spacing of ap-proximately 5 km for use as cadastral control at the governorate level.

• Finally, replace the existing Egyptian Mercator grid with a new modified UTM coordinate system.

Figure (1): The HARN & NACN Networks

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http://gge.unb.ca/Resources/PPP/index.htm

ftp://garner.ucsd.edu/pub/rinex/2015/100/



Table (2): ITRF2008 Station Positions at Epoch 2005.0 and Velocities DOMES

SITE

X/Vx Y/Vy Z/Vz Sigmas

----------------------m/m/y--------------------- 35001M002 Rabat RABT 5255617.683 -631745.687 3546322.552 0.001 0.001 0.001 35001M002 -0.0088 0.0174 0.0142 0.001 0.000 0.0001 33201M001 MALINDI MALI 4865366.354 4110737.599 -331121.569 0.001 0.001 0.001 33201M001 -0.0172 0.02 0.0167 0.001 0.0001 0.0000 20703S001 Mitz. RAMON RAMO 4514721.855 3133507.841 3228024.716 0.001 0.001 0.001 20703S001 -0.0205 0.0141 0.0177 0.001 0.0001 0.0001 14302M001 NICOSIA Ath. NICO 4359415.713 2874117.066 3650777.829 0.001 0.001 0.001 14302M001 -0.0179 0.0116 0.0126 0.001 0.0001 0.0001

Table (3): DATA SET EXPRESSED IN ITRF2008 FRAME STATION POSITIONS AND VELOCITIES AT EPOCH 2015/04/10

DOMES NB SITE NAME ID SOLN X Y Z SIGMA

x SIGMA y SIGMA z

35001M002 RABAT RABT 1 5255617.683 -631745.687 3546322.552 0.001 0.001 0.001

33201M001 MALINDI MALI 1 4865366.177 4110737.805 -331121.398 0.001 0.001 0.001

14302M001 NICOSIA-ATHALASSA NICO 1 4359415.525 2874117.189 3650777.949 0.001 0.001 0.001

20703S001 Mitzpe Ramon RAMO 1 4514721.645 3133507.986 3228024.898 0.001 0.001 0.001

Table (4): the updated positioning for four IGS stations defined in ITRF2008 epoch 2015.274 by IGS & PPP

Rabat Sol. Type X Y Z

PPP- Solution 5255617.590 -631745.508 3546322.700 IGS-Solution 5255617.593 -631745.508 3546322.698 Differences -0.003 0.000 0.002

Mali

Sol. Type X Y Z PPP- Solution 4865366.174 4110737.798 -331121.393

IGS-Solution 4865366.177 4110737.805 -331121.398 Differences -0.003 -0.007 0.005

Nico

Sol. Type X Y Z PPP- Solution 4359415.522 2874117.172 3650777.950 IGS-Solution 4359415.525 2874117.189 3650777.949 Differences -0.003 -0.017 0.001

Ramo

Sol. Type X Y Z PPP- Solution 4514721.636 3133507.978 3228024.886 IGS-Solution 4514721.641 3133507.982 3228024.891 Differences -0.005 -0.004 -0.005

Table (5): The differences between DGPS & PPP solutions for the observed Stations

St.

DGPS Sol.

PPP Sol.

Differences bet DGPS & PPP

X Y Z X Y Z dX dY dZ

PHLW 4728141.180 2879662.608 3157147.159 4728141.180 2879662.608 3157147.159 0.000 0.000 0.000

0Z18 4657081.787 2807150.058 3322370.152 4657081.784 2807150.059 3322370.156 0.003 -0.001 -0.004

0Z20 4796793.729 2651830.764 3250924.993 4796793.697 2651830.738 3250924.970 0.032 0.026 0.023

0Z89 4745737.252 2795140.347 3205858.805 4745737.246 2795140.341 3205858.797 0.006 0.006 0.008

0Z94 4739314.560 2828743.551 3186027.207 4739314.553 2828743.544 3186027.199 0.007 0.007 0.008

Burg 4765954.276 2704546.183 3252949.202 4765954.269 2704546.174 3252949.193 0.007 0.009 0.009

O1 4728219.038 2879743.411 3156930.682 4728219.033 2879743.402 3156930.676 0.005 0.009 0.006

The ITRF1994 was transferred to Egypt’s HARN net-work by connecting it with four IGS stations, namely

MATE (Italy), KIT3 (Uzbekistan), HART (South Afri-ca) and MASP in (Canary Island). Each HARN’s sta-

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tion was observed for six sessions, every session was 6 hours with 30 seconds epoch interval. The observation time was planned to produce 1:10,000,000 (Order A) for HARN and 1:1,000,000 (Order B) for NACN rela-tive network accuracy standard between stations. The results of analyzing both of them were defined in ITRF1994 epoch 1996.

To see for what extent can the PPP be an alterna-tive for the differential techniques and its impact in analyzing the geodetic applications that need an ulti-mate accuracy like the National High Accuracy Refer-ence Networks, a critical example is given to demon-strate this study. The example is concerned with ana-lyzing a part of Egypt HARN and NACN (National Agriculture Cadastre) Networks that is located in and around Nile Delta. The geometric location of this part is illustrated in figure (2) and the position of the aforementioned points as given in HARN analysis report [8] is depicted in table (6). Additionally, this section deals with the computing techniques that are used in transferring the terrestrial frame from epoch to epoch in to different frames.

Table (6): The coordinates of chosen points of the HARN and

ITRF 1994, epoch 1996 (Scott, 1997)

Station X Y Z

OZ94 4745737.755 2795140.173 3205858.575

OZ89 4739315.089 2828743.36 3186026.976

OZ18 4657082.606 2807149.887 3322369.803

OZ20 4796794.204 2651830.557 3250924.750

Three days campaigns were conducted in June 2015 from 3 to 6, to convert this part of HARN & NACN network in the most recent ITRF available frame at the epoch of observation campaigns, namely ITRF 2008 epoch 2015.422. However, we use the aforementioned approach, equation (7) in transferring the PPP solu-tion of the specified part of HARN to the ITRF 2000 epoch 2000, utilizing the three parameters of Nubian plate as defined by ITRF2005-PMM [3].,

Figure (2): The location of the used part of Egypt HARN & NACN

Table (7): The Part of HARN & NACN network updated in ITRF2000

ST.

PPP Results Coordinate at Epoch 2015.422 Transformed PPP Coordinates at ITRF2008

Epoch 2005

X Y Z X Y Z PHLW 2879662.632 2879662.632 3157147.186 2879662.851 2879662.483 3157147.019 0Z18 4657081.784 2807150.059 3322370.156 4657082.003 2807149.91 3322369.989 0Z20 4796793.697 2651830.738 3250924.970 4796793.916 2651830.589 3250924.803 0Z89 4745737.246 2795140.341 3205858.797 4745737.465 2795140.192 3205858.63 0Z94 4739314.553 2828743.544 3186027.199 4739314.772 2828743.395 3186027.032 Burg 4765954.269 2704546.174 3252949.193 4765954.488 2704546.025 3252949.026 O1 4728219.033 2879743.402 3156930.676 4728219.252 2879743.253 3156930.509

The evaluation strategy is based upon:

A. Evaluating the IGS stations that were used in transferring the ITRF to HARN, by using their

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published ITRF2008 Epoch2015.422 coordinates values and the related transformation parameter to ITRF1994 Epoch1996 and compares the trans-ferred values by the reported values of [7].

B. Transferring the values of HARN & NACN net-works that were defined in ITRF2008 epoch 2005 to the original ITRF frame of HARN, namely ITRF1994 epoch 1996 and compare the resulted values with the original coordinate’s values giv-en by [8]. The aforementioned transformation is performed by exploiting the published 14 trans-formation parameters between different ITRF’s Frames by IGS [9]. However, the transformation process from ITRF 2008 epoch 2015.422 to ITRF 1994 epoch 1996 will be performed in the follow-ing steps:

1. Transforming the PPP values of HARN & NACN networks that defined in ITRF2008 epoch 2015.422 to ITRF2008 Epoch2005 using the published Absolute Pole Cartesian angular Velocity for Nu-bian Plate, as outlined before.

2. Transferring the ITRF2008 Epoch2005 to ITRF1994 Epoch 2000 using the pub-lished parameters in table (8).

3. Updating the values specified in the table (8) to be in Epoch 1996 instead of Epoch2000.

4. Compute the differences

4.1 EVALUATING THE IGS STATIONS THAT WAS USED IN TRANSFERRING THE ITRF TO HARN

Before digging into applying the above proce-dures, a check for the published transformation pa-rameters are done. This step is so necessary to check the quality of the published data by IGS as well as to

see the size of errors embedded in the stations that were used by [8] in transferring the ITRF1994 frame to Egypt’s HARN, namely MATE (Italy), KIT3 (Uzbeki-stan), HART (South Africa) and MASP in (Canary Island). Table (9) depicts the coordinates of the four IGS stations defined in ITRF1994 Epoch 1996 as given by [8] and the published by IGS in ITRF2008, Epoch2005.

It was stated in http://itrf.ign.fr/rel_trs.php that the standerd relation of transformation between two reference systems is an Euclidian similarity of seven parameters : three translation components , one scale factor , and three rotation angles , designated respec-tively ,T1, T2, T3, D, R1, R2, R3, and their first times der-ivations : T1∙ , T2∙ , T3∙ , D, R1

∙ , R2∙ , R3

∙ .The transformation of coordinate vector X1, expressed in a reference sys-tem (1), into a coordinate vector X2, expressed in a reference system (2), is given by the following equa-tion: 𝑿𝐑 = 𝑿𝟎 + 𝑻+ 𝑫𝑿𝟎 +𝑹 𝑿𝟎 (8)

With: T = �T1T2T3� and R = �

0 −R3 R2R3 0 −R1−R2 R1 0

� It is assumed that equation (7) is linear for sets of

station coordinates provided by space geodetic tech-nique (origin difference is about a few hundred me-ters, and differences in scale and orientation are of 10-5 level). Generally, X1, X2, T, D, R are function of time. Differentiating equation (7) with respect to time gives:

𝑿𝐑∙ = 𝑿𝟎

∙ + 𝑻∙ + 𝑫∙𝑿𝟎 +𝑫 𝑿𝟎∙ +𝑹∙𝑿𝟎 +𝑹 𝑿𝟎

∙ (9) D and R are of 10-5 level and D∙ is about 10 cm per year, the terms D X1∙ and R X1∙ are negligible which rep-resent about 0.0 mm over years. Therefore equation (9) could be written as:

𝑿𝐑∙ = 𝑿𝟎

∙ + 𝑻∙ + 𝑫∙𝑿𝟎+𝑹∙𝑿𝟎 (10)

Table (8): Transformation parameters Between ITRF2008 Epoch 2005 to ITRF 1994 Epoch 2000

EPOCH R1 .𝟎𝟎𝟎′′

R1 .𝟎𝟎𝟎′′

R1 .𝟎𝟎𝟎′′

D Ppb

T3 mm

T2 mm

T1 mm

SOLUTION UNITS……

𝐑𝐑. . 001′′/Y

𝐑𝐑. . 001′′/Y

𝐑𝟎. . 001′′/Y

𝐃. Ppb/Y

𝐓𝐑. mm/Y

𝐓𝐑. mm/y

𝐓𝟎. mm/y

RATES UNITS……

2000 0.06 0.02

0.00 0.00

0.00 0.00

2.92 0.09

-33.2 -3.2

2.6 -0.05

4.8 0.1

ITRF94 rates

Table (9): The coordinate values of the IGS four stations in ITRF1994, Epoch 1996 and the published coordinate

values for the nominated IGS stations in ITRF2008 Epoch2005 Station ITRF2008 Epoch2005 ITRF1994 Epoch 1996 (as given by Scott, 1997) MATE 4641949.557 1393045.422 4133287.465 4641949.737 1393045.262 4133287.317 KIT3 1944945.139 4556652.244 4004326.007 1944945.390 4556652.199 4004325.973

HART 5084625.288 2670366.383 -2768494.401 5084625.460 2670366.404 -2768494.470 MAS1 5439192.215 -1522055.484 2953454.847 5439192.277 -1522055.641 2953454.694

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http://itrf.ign.fr/rel_trs.php



The four stations in table (7) were transferred from ITRF2008 Epoch2005 to ITRF1994 Epoch2000 using the transformation parameters given in table (8) and equation (8). The results were demonstrated in table (10). Also the velocities of the specified IGS stations in ITRF1994 were also depicted in table (10). To transfer the computed IGS coordinates from Epoch2000, as: t0= 2000, to the epoch of the HARN solu-tions, ITRF 1994 Epoch1996 as t, equation (7) was used. The results of the transformation were given in table (11). To see the differences between the original coordinate val-ues of the used IGS four stations as given by Scott (1997), defined in ITRF1994 Epoch1996, as outlined in table (7), the differences between the two ITRFs were computed and recorded in table (11). As it is shown in table (11), in spite of we have already used only in the previous processing the published values and models as specified by IGS, one can see a tolerance ranged between -8.6 cm to 14.6 cm. The reasons behind these differences are mostly returning to the limited number of stations, only 13 stations - see figure (3)-, that were used in realizing the ITRF94 that leads to sub-optimal stations distribution and small discontinuities between IGS realizations of ITRF, as clarified by [10].

4.2 TRANSFERRING THE SOLVED PPP PART OF HARN NETWORK TO THE ITRF 1994 EPOCH 1996 Firstly, transfer the tested part of HARN and NACN

from ITRF2008 epoch2005, specified in table (5), to HARN ITRF1994 epoch 2000, with the aforementioned steps by using equation (8) and table (8). The computation results are given in table (11).

Figure (3): Station set (13) used for IGS Realization of ITRF

92-93-94

Table (10): The transferred coordinate values of the four stations to ITRF1994 Epoch2000 Station ITRF1994 Epoch2000 Velocity m/y MATE 4641949.557 1393045.429 4133287.444 -0.019 0.020 0.012 KIT3 1944945.149 4556652.260 4004325.985 -0.028 0.016 0.006 HART 5084625.308 2670366.394 -2768494.442 -0.002 0.016 0.018 MAS1 5439192.236 -1522055.486 2953454.822 0.001 0.015 0.015

Table (11): The differences between the published coordinate values of the four IGS stations & the reported values by (Scott, 1997) in ITRF1994 Epoch1996

St.

ITRF1994 Epoch1996 transferred from IGS published values in ITRF2008

Epoch2005 ITRF1994 Epoch1996 as reported by

Scott (1997) Differences

X Y Z X Y Z dX dY dZ

MATE 4641949.633 1393045.348 4133287.396 4641949.737 1393045.262 4133287.317 0.104 -0.086 -0.079 KIT3 1944945.261 4556652.195 4004325.959 1944945.390 4556652.199 4004325.973 0.129 0.004 0.014 HART 5084625.314 2670366.328 -2768494.514 5084625.460 2670366.404 -2768494.470 0.146 0.076 0.044 MAS1 5439192.236 -1522055.548 2953454.761 5439192.277 -1522055.641 2953454.694 0.041 -0.093 -0.067

Table (11): The Results of Transformation the HARN to ITRF 1994 Epoch 1997

St. PPP at ITRF2008 Epoch 2005 PPP at ITRF1994Epoch 2000 X Y Z X Y Z

PHLW 4728141.399 2879662.459 3157146.992 4728141.418 2879662.470 3157146.968 0Z18 4657082.003 2807149.910 3322369.989 4657082.021 2807149.921 3322369.966 0Z20 4796793.916 2651830.589 3250924.803 4796793.935 2651830.599 3250924.779 0Z94 4745737.465 2795140.192 3205858.630 4745737.484 2795140.203 3205858.606 0Z89 4739314.772 2828743.395 3186027.032 4739314.791 2828743.406 3186027.008 Burg 4765954.488 2704546.025 3252949.026 4765954.507 2704546.036 3252949.002 O1 4728219.252 2879743.253 3156930.509 4728219.271 2879743.264 3156930.485

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To transfer the resulted coordinate’s values of the tested part of HARN from ITRF1994 Epoch2000 to ITRF1994 Epoch 1996, there is a need to define the Nubian Plate Velocity in the same ITRF1994. Equation (10) can be used in computing the velocities of the Egyptian stations in ITRF1994, provided that the stations velocities should be defined in ITRF2008. This can be performed by applying equation (4) and table (4). The resulted velocities are rep-resented in table (12). So the HARN stations can be con-verted to ITRF1994 Epoch1996, by using equation (7) and considering Epoch2000 as: t0= 2000, and Epoch1996 as t = 1996. The results are depicted also in table (12). The dif-ferences between the reported part of HARN by Scott (1997) and the computed part based on PPP techniques and the IGS related transformation parameters and veloci-ties defined in IREF1994 Epoch 1996 is displayed in table (13). As it is shown in the table, the differences in X-component ranged from 34 to 37 cm, except 0Z18 that was partially destroyed, and Y-component ranged from -8 cm to -11 cm and for Z-component, the differences were ranged between -7 cm and -8 cm, except 0Z18. Finally, one can see that size of error budget that affects the original processing of Egyptian HARN network which stem from connecting parts of Egyptian HARN with four stations of IGS that were far away from EGYPT, namely HART, KIT3, MAS1 and MAT, forming very long baselines as depicted in figure (4). Also the errors in the definition of ITRF1994 itself, that was reached 7 to14 cm as computed

in chapter 4.1. Additionally, within the plate boundary regions (e.g. in the vicinity of the African Rift and in the northern coastal areas) there will be inter-seismic defor-mation of up to a 3-4 mm/year which will not be modeled using a rigid plate transformation model [2].

5. CONCLUSIONS To evaluate the performance of the PPP processing engine, several PPP tests on several African IGS station were performed to transfer them to ITRF2005 Epoch 2000 using three parameters kinematic rigid plate model and comprising the results of the IGS stations published IERS values in the same Epoch. The differences were just a few centimeters. The results confirm the usability of PPP with the kinematic rigid plate model in updating the frame. By the aforementioned transformation parameters, the difference between the computed and the given origi-nal values computed by [8], in X-component ranged from 34 to 37 cm, and Y-component ranged from -8 to -11 cm and Z-component, the differences were ranged between -7 and -8 cm. As a closing conclusion for the overall results, one can say that PPP is the most feasible factor in per-forming datum maintenance by time and cost. The Egyp-tian HARN & NACN Networks need to update their frame, to be the most recent one either by PPP or tradi-tional approach.

Table (12): The computed velocities and the transferred coordinate values to ITRF 94

Epoch 96 of the specified part of the Egyptian HARN

St. Velocities at ITRF1994 m/y PPP at ITRF1994Epoch 1996

VX VY VZ X Y Z PHLW -0.0187 0.0149 0.0121 4728141.343 2879662.53 3157147.016 0Z18 -0.0190 0.0146 0.0119 4657081.945 2807149.979 3322370.013 0Z20 -0.0182 0.0151 0.0122 4796793.862 2651830.66 3250924.828 0Z94 -0.0186 0.0150 0.0121 4745737.409 2795140.263 3205858.655 0Z89 -0.0187 0.0149 0.0121 4739314.716 2828743.466 3186027.057 Burg -0.0184 0.0150 0.0122 4765954.433 2704546.096 3252949.051 O1 -0.0187 0.0149 0.0121 4728219.196 2879743.324 3156930.533

Table (13): The Difference between the computed PPP HARN transferred to ITRF 94 Epoch 96 and the given values at the same epoch as computed by Scott (1997)

St. PPP Sol transferred to ITRF1994Epoch 1996 ITRF 1994, epoch 1996 (Scott, 1997). Differences X Y Z X Y Z dX dY dZ

0Z18 4657081.945 2807149.979 3322370.013 4657082.606 2807149.887 3322369.803 0.661 -0.092 -0.210 0Z20 4796793.862 2651830.660 3250924.828 4796794.204 2651830.557 3250924.75 0.342 -0.103 -0.078 0Z94 4745737.409 2795140.263 3205858.655 4745737.755 2795140.173 3205858.575 0.346 -0.090 -0.080 0Z89 4739314.716 2828743.466 3186027.057 4739315.089 2828743.36 3186026.976 0.373 -0.106 -0.081

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6. REFERENCES [1] Chang, C. and Tseng, L., (1998) : A Geocentric Reference

System in Taiwan , Survey Review, Department of Survey-ing and Mapping Engineering Chung Cheng Institute of Technology, Taiwan, ROC.

[2] Stanaway, R., and Roberts, C. (2009): A Simplified Pa-rameter Transformation Model from ITRF2005 to any Static Geocentric Datum (e.g. GDA94), Proceedings from Interna-tional Global Navigation Satellite Systems Society IGNSS Symposium 2009, Surfers Paradise, Qld, Australia 1 – 3 De-cember, 2009

[3] Altamimi, Z., Collileux, J., Legrand, J., Garayt, B., and Boucher, C. (2007); ITRF2005: A new release of the Inter-national Terrestrial Reference Frame based on time series of station positions and Earth Orientation Parameters, Journal of Geophysical Research, Vol. 112, B09401, doi:10.1029/2007JB004949

[4] IERS, (2010): http://itrf.ensg.ign.fr/ITRF_solutions/2005/doc/ITRF2005_GPS.SSC.txt (accessed, 11th November, 2010).

[5] Altamimi Z, Métivier L, Collilieux X (2012): ITRF2008 plate motion model. J Geophys Res 117, B07402. doi: 10.1029/2011JB008930

[6] Elhattab, A. (2014): Assessment of PPP for establishment of CORS network for municipal surveying in Middle East. Port Said University, Faculty of Engineering, Egypt.

[7] Altamimi, Z. (2006): IGS reference frames: Status and fu-ture improvements, Institute Geographique National, France.

[8] Scott, M. (1997): Results of Final Adjustment of New Na-tional Geodetic Network, Geodetic Advisor for the Egyptian Survey Authority

[9] John D. and Jim (2004): International Terrestrial Refer-ence Frame (ITRF) to GDA94 Coordinate Transformations Minerals and Geohazards Division Geosciences Australia Version 01.03.2004

[10] Ferland, R. and Kouba, J., (1996): IGS ITRF Realization and Transformations. Geodetic Survey Division Natural Re-sources Canada (NRCan) Ottawa, Canada K1A OE9.

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Evaluating the Egyptian HARN Network by GNSS Precise Point Positioning “PPP”

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